A naked triple is naked pair at three cells instead of two, with one wrinkle: none of the three cells needs to show all three digits. As long as three cells in a unit between them only ever use three digits total — two candidates here, three there, two over there, as long as the union is exactly three digits — those three digits are locked to those three cells.

The part that trips people up

With a naked pair, both cells show the exact same two candidates, so it’s easy to spot. A naked triple doesn’t require that: one cell might show 5, another 9, a third 9 — no cell shows all three digits, but together they only ever mention 2, 5, and 9. That’s still a valid triple, because wherever those three digits land, they land in these three cells.

Worked example

8
147
9
2
6
157
457
3
47
5
47
24
8
9
3
247
1
6
3
167
126
147
145
157
257
8
9
7
134
145
9
2
158
38
6
45
1246
1346
8
1367
15
1567
9
247
457
26
9
56
367
58
4
38
27
1
469
5
3
146
148
168
467
479
2
1469
8
146
5
7
2
46
49
3
46
2
7
46
3
9
1
5
8

r4c6, r5c5, r6c5 in box 5 share only 1, 5, 8 between them, so those digits can be removed from the rest of box 5.

As with a naked pair, the three cells holding the triple don’t change — the elimination clears those three digits from every other cell in the same row, column, or box.

How to find one quickly

Shortlist the cells in a unit with two or three candidates each — a cell with four or more can’t be part of a naked triple. Take any three of those cells and check the total number of distinct digits across all three. If it’s exactly three, you’ve found one, regardless of how the digits are distributed between the cells.

This is the direct extension of naked pair and hidden pair — same logic, one cell wider. Beyond this, the board usually needs to look across more than one unit at a time, which is what X-Wing does.

Puzzles at Hard are the first level built around needing this.